Speed or torque control performance and accuracy of induction motors are improved with a speed-sensorless vector control method for some restricted environment setting a speed sensor in order to reduce the cost or to simplify the wiring. Generally, the speed feedback of the conventional method is produced by some kind of speed-adaptive flux observers, which are introduced by:
Document 1: C. Nitayotan and S. Sangwongwanich, “A Filtered Back EMF Based Speed Sensorless Induction Motor Drive,” Proceeding of IEEE-IAS Annu. Meeting, Chicago, Ill., 2001, pp. 1224-1231; and
Document 2: S. Suwankawin and S. Sangwongwanich, “A Speed-Sensorless IM Drive With Decoupling Control and Stability Analysis of Speed Estimation,” IEEE Trans. Ind. Electron., vol. 49, no. 2, March/April 2002, pp. 444-55.
Please refer to FIG. 1, which is a schematic diagram showing a conventional vector control system for a speed-sensorless induction motor. As shown, the vector control system 10 includes a power supply unit 113, an inverter 102, an induction motor 101, a current detection unit 103, a three/two-phase transformation unit 105, a two/three-phase transformation unit 104, a speed-adaptive magnetic flux observer 108, a static/synchronous conversion unit 107, a speed controller 112, a magnetic flux controller 111, a current controller 109, a current controller 110, and a synchronous/static conversion unit 106.
The power supply unit 113 provides a DC bus voltage to the inverter 102. The inverter 102 receives a three-phase control voltage {right arrow over (u)}s3—1 and the DC bus voltage and uses the three-phase control voltage {right arrow over (u)}s3—1 to control the DC bus voltage for driving the induction motor 101 coupled to the inverter 102. The current detection unit 103 detects a three-phase stator current of the stator of the induction motor 101 and produces a three-phase detected current {right arrow over (i)}s3—1. The three/two-phase transformation unit 105 receives the three-phase detected current {right arrow over (i)}s3—1 and transforms the three-phase detected current {right arrow over (i)}s3—1 into a two-phase current {right arrow over (i)}s—1 under a static reference coordinate system of the induction motor 101. The two/three-phase transformation unit 104 receives a two-phase voltage {right arrow over (u)}s—1 and transforms the two-phase voltage {right arrow over (u)}s—1 into the three-phase control voltage {right arrow over (u)}s3—1 under the static reference coordinate system, wherein the three-phase control voltage {right arrow over (u)}s3—1 is provided to the inverter 102. The speed-adaptive magnetic flux observer 108 receives the two-phase current {right arrow over (i)}s—1 and the two-phase voltage {right arrow over (u)}s—1 and produces an estimated rotor angular speed {circumflex over (ω)}r—1, an estimated magnetizing current îm—1, and an estimated magnetizing-axis angular position {circumflex over (θ)}m—1, of the estimated magnetizing current îm—1, which are estimated properties of the induction motor 101.
The static/synchronous conversion unit 107 receives the two-phase current {right arrow over (i)}s—1 and the estimated magnetizing-axis angular position {circumflex over (θ)}m—1 and converts the two-phase current {right arrow over (i)}s—1 under the static reference coordinate system into both a q-axis current (torque current) isq—1 and a d-axis current (magnetizing-axis current) isd—1 under a synchronous reference coordinate system of the induction motor 101 according to the estimated magnetizing-axis angular position {circumflex over (θ)}m—1. The speed controller 112 receives a rotor angular speed command ωr—1* and the estimated rotor angular speed {circumflex over (ω)}r—1 and matches the rotor angular speed command ωr—1* with the estimated rotor angular speed {circumflex over (ω)}r—1 for producing a torque current command isq—1*. The magnetic flux controller 111 receives a magnetizing current command im—1* and the estimated magnetizing current îm—1 and matches the magnetizing current command im—1* with the estimated magnetizing current îm—1 for producing a magnetizing-axis current command isd—1*.
The current controller 109 receives the torque current command isq—1* and the torque current isq—1 and matches the torque current command isq—1* with the torque current isq—1 for producing a torque-axis voltage command u*sq—1*. The current controller 110 receives the magnetizing-axis current command isd—1* and the magnetizing-axis current isd—1 and matches the magnetizing-axis current command isd—1* with the magnetizing-axis current isd—1 for producing a magnetizing-axis voltage command usd—1*.
The synchronous/static conversion unit 106 receives the estimated magnetizing-axis angular position {circumflex over (θ)}m—1 and both the torque-axis voltage command usq—1* and the magnetizing-axis voltage command usd—1* under the synchronous reference coordinate system and converts both the torque-axis voltage command usq—1* and the magnetizing-axis voltage command usd—1* into the two-phase voltage {right arrow over (u)}s—1 under the static reference coordinate system. It is noted that the estimated magnetizing-axis angular position {circumflex over (θ)}m—1 received by both the static/synchronous conversion unit 107 and the synchronous/static conversion unit 106 is fed back from the speed-adaptive magnetic flux observer 108.
Please refer to FIG. 2, which is a schematic diagram showing an equivalent circuit of the induction motor. The denoting meanings of respective symbols are shown as follows.
ūs: stator input voltageīs: stator currentRs: stator-winding resistanceLσ: stator-winding leakage inductanceω1: synchronous angular frequency of thestator rotating magnetic field(stator angular frequency)Lm: magnetizing inductanceīm: magnetizing currentēm: induced voltage (back-EMF)ωr: rotor angular speedRs: rotor resistanceīr: rotor current
Please refer to FIG. 3, which is a schematic diagram showing a mechanical model of the induction motor. The denoting meanings of respective symbols are shown as follows.
Te: electromagnetic torque of the motor
TL: load torque of the motor
J: rotational inertia of the mechanical load
ωr: rotor angular speed
The angular position of the magnetizing flux or current of the induction motor may be calculated according to the above-mentioned documents by Equation 1.{circumflex over (θ)}m=∫ω1dt  Equation 1
wherein ω1 is the stator angular frequency, which can be calculated by Equation 2.ω1={circumflex over (ω)}r+ωslip  Equation 2
wherein {circumflex over (ω)}r is the estimated rotor angular speed of the induction motor, and the slip ωslip may be calculated by Equation 3.
                              ω          slip                =                              1                          T              r                                ·                                                    i                ^                            sq                                                      i                ^                            m                                                          Equation        ⁢                                  ⁢        3            
wherein
      T    r    =            L      m              R      r      is the rotor time constant, and
            i      ^        sq    =                              i                      s            ⁢                                                  ⁢            β                          ⁢                              i            ^                                m            ⁢                                                  ⁢            α                              -                        i                      s            ⁢                                                  ⁢            α                          ⁢                              i            ^                                m            ⁢                                                  ⁢            β                                              i        ^            m      is the estimated torque current.
In the computation formula of the estimated torque current îsq, îm is the amplitude of the estimated magnetizing current, îmα, îmβ are the orthogonal two-axis components of the estimated magnetizing current îm under the two-phase static reference coordinate system, and îmα, îmβ are the orthogonal two-axis components of the stator current under the two-phase static reference coordinate system. In Equation 3, the estimated torque current îsq may also be replaced with the real torque current isq, and the estimated magnetizing current îm may also be replaced with the magnetizing current command îm.
The speed-adaptive magnetic flux observers presented in the above documents are based on the fundamental model of the induction motor. When the magnitude of the stator angular frequency is less than a minimum of a positive angular frequency around zero angular frequency, it is impossible to estimate the motor speed. In order to avoid working in the above-mentioned range of the very low stator angular frequency, a flux-weakening method is presented by:
Document 3: M. Depenbrock, C. Foerth, and S. Koch, “Speed Sensorless Control Of Induction Motors At Very Low Stator Frequencies,” The 8th European Power Electronics Conf. (EPE), Lausanne, Switzerland, 1999; and
Document 4: Hisao Kubota, Ik-uya Sato, Yuichi Tamura, Kouki Matsuse, Hisayoshi Ohta, and Yoichi Hori, “Regenerating-Mode Low-Speed Operation of Sensorless Induction Motor Drive With Adaptive Observer,” IEEE Transactions on Industry Applications, Vol. 38, No. 4, July/August 2002, pp. 1081-1086.
The flux-weakening method used in the Documents 3 and 4 increases the slip in order to avoid operating around zero angular frequency. However, the flux weakening will decrease the load capability, so that the flux-weakening method is not applicable for some heavy-load application. Furthermore, for some motor with a very small slip, the stator angular frequency can be hardly increased any more. So for general consideration, the stator angular frequency should be limited to be greater than a minimum angular frequency in order to avoid operating around zero angular frequency.
If the stator angular frequency is limited to be greater than a minimum angular frequency, it can be seen from Equation 2 that if only the stator frequency is limited in FIG. 1, Equation 3 cannot be guaranteed; that is, Equation 3 is prohibited according to the vector control principles of the induction motor. Therefore, how to make the stator angular frequency, responding to the load and speed reference variation, be close to that of the conventional vector control system shown in FIG. 1 and how to skip zero stator angular frequency become the primary motive of the present invention.